As in our paper [1]}, we use the following notations.
3D Young diagram \(\pi \)  may have many ways to get by adding box, for example, there are two ways to get 3D Young diagram \((2,1)\) , which are
\(&&(1)\rightarrow (1,1)\rightarrow (2,1),\\&&(1)\rightarrow (2)\rightarrow (2,1),\) 
